Question

In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ =...

In a regression analysis involving 30 observations, the following estimated regression equation was obtained.

ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4

For this estimated regression equation, SST = 1,815 and SSR = 1,780. (a) At α = 0.05, test the significance of the relationship among the variables.

State the null and alternative hypotheses.

H0: β0 = β1 = β2 = β3 = β4 = 0

Ha: One or more of the parameters is not equal to zero.

H0: One or more of the parameters is not equal to zero.

Ha: β0 = β1 = β2 = β3 = β4 = 0

H0: One or more of the parameters is not equal to zero.

Ha: β1 = β2 = β3 = β4 = 0

H0: β1 = β2 = β3 = β4 = 0

Ha: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.) p-value =

State your conclusion.

Do not reject H0. We conclude that the overall relationship is not significant.

Do not reject H0. We conclude that the overall relationship is significant.

Reject H0. We conclude that the overall relationship is significant.

Reject H0. We conclude that the overall relationship is not significant.

Suppose variables x1 and x4 are dropped from the model and the following estimated regression equation is obtained.

ŷ = 11.1 − 3.6x2 + 8.1x3

For this model, SST = 1,815 and SSR = 1,725.

(b) Compute SSE(x1, x2, x3, x4). SSE(x1, x2, x3, x4) =

(c) Compute SSE(x2, x3). SSE(x2, x3) =

(d) Use an F test and a 0.05 level of significance to determine whether x1 and x4 contribute significantly to the model. State the null and alternative hypotheses.

H0: One or more of the parameters is not equal to zero.

Ha: β1 = β4 = 0 H0: β1 = β4 = 0 Ha: One or more of the parameters is not equal to zero.

H0: One or more of the parameters is not equal to zero.

Ha: β2 = β3 = 0

H0: β2 = β3 = 0

Ha: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.) p-value =

State your conclusion.

Reject H0. We conclude that x1 and x4 contribute significantly to the model.

Do not reject H0. We conclude that x1 and x4 contribute significantly to the model.

Reject H0. We conclude that x1 and x4 do not contribute significantly to the model.

Do not reject H0. We conclude that x1 and x4 do not contribute significantly to the model.

Homework Answers

Answer #1

a)

H0: β0 = β1 = β2 = β3 = β4 = 0

Ha: One or more of the parameters is not equal to zero

SSE =SST-SSR= 35.0
MSR=SSR/k= 445.0
MSE=SSE/(n-k-1)= 1.4
F =MSR/MSE = 317.86
p value=0.0000

Reject H0. We conclude that the overall relationship is significant.

b)

SSE(x1,x2,x,3,x4) = 35

c)

SSE(x2x3) = 90

d)

H0: β1 = β4 = 0 Ha: One or more of the parameters is not equal to zero.

F = ((90-35)/2)/(35/25)= 19.64
p value =0.000

Reject H0. We conclude that x1 and x4 contribute significantly to the model.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ =...
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation, SST = 1,835 and SSR = 1,800. (a)At α = 0.05, test the significance of the relationship among the variables.State the null and alternative hypotheses. -H0: One or more of the parameters is not equal to zero. Ha: β0 = β1 = β2 = β3 = β4 = 0 -H0:...
You may need to use the appropriate technology to answer this question. In a regression analysis...
You may need to use the appropriate technology to answer this question. In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation, SST = 1,835 and SSR = 1,790. (a) At α = 0.05, test the significance of the relationship among the variables. State the null and alternative hypotheses. H0: One or more of the parameters is not equal to...
In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ =...
In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ = 25.2 + 5.5x1 For this estimated regression equation SST = 1,550 and SSE = 530. (a) At α = 0.05, test whether x1  is significant.State the null and alternative hypotheses. H0: β1 ≠ 0 Ha: β1 = 0 H0: β0 ≠ 0 Ha: β0 = 0    H0: β0 = 0 Ha: β0 ≠ 0 H0: β1 = 0 Ha: β1 ≠ 0 Find the value...
In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ =...
In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ = 25.2 + 5.5x1 For this estimated regression equation SST = 1,600 and SSE = 550. (a) At α = 0.05, test whether x1is significant.State the null and alternative hypotheses. H0: β0 = 0 Ha: β0 ≠ 0 H0: β0 ≠ 0 Ha: β0 = 0    H0: β1 ≠ 0 Ha: β1 = 0 H0: β1 = 0 Ha: β1 ≠ 0 Find the value...
In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ =...
In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ = 25.2 + 5.5x1 For this estimated regression equation SST = 1,600 and SSE = 550. (a) At α = 0.05, test whether x1 is significant. State the null and alternative hypotheses. H0: β0 = 0 Ha: β0 ≠ 0H0: β0 ≠ 0 Ha: β0 = 0    H0: β1 ≠ 0 Ha: β1 = 0H0: β1 = 0 Ha: β1 ≠ 0 Find the value of...
You may need to use the appropriate technology to answer this question. In a regression analysis...
You may need to use the appropriate technology to answer this question. In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ = 25.2 + 5.5x1 For this estimated regression equation SST = 1,550 and SSE = 590. (a) At α = 0.05, test whether x1 is significant. State the null and alternative hypotheses. H0: β0 ≠ 0 Ha: β0 = 0 H0: β1 = 0 Ha: β1 ≠ 0    H0: β0 = 0 Ha:...
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ =...
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation, SST = 1,805 and SSR = 1,770 a. Find the value of the test statistic. (Round your answer to two decimal places.) _________ b. Suppose variables x1 and x4 are dropped from the model and the following estimated regression equation is obtained. ŷ = 11.1 − 3.6x2 + 8.1x3 Compute...
The following estimated regression equation based on 10 observations was presented. ŷ = 21.1370 + 0.5509x1...
The following estimated regression equation based on 10 observations was presented. ŷ = 21.1370 + 0.5509x1 + 0.4980x2 Here, SST = 6,724.125, SSR = 6,222.375, sb1 = 0.0814, and sb2 = 0.0565. 1. Compute MSR and MSE. (Round your answers to three decimal places.) MSR= MSE= 2. Compute F and perform the appropriate F test. Use α = 0.05. 2a. State the null and alternative hypotheses. (a) H0: β1 = β2 = 0 Ha: One or more of the parameters...
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ =...
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 18.9 + 3.2x1 − 2.2x2 + 7.8x3 + 2.9x4 (a) Interpret b1 in this estimated regression equation. b1 = 7.8 is an estimate of the change in y corresponding to a 1 unit change in x3 when x1, x2, and x4 are held constant.b1 = 3.2 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2,...
The following regression output was obtained from a study of architectural firms. The dependent variable is...
The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars.   Predictor Coeff SE Coeff t p-value   Constant 8.366 3.002 2.787 0.010 X1 0.225 0.301 0.748 0.000   X2 –1.216 0.538 –2..260 0.028   X3 -0.070 0.377 –0.186 0.114   X4 0.552 0.322 1.714 0.001   X5 -0.049 0.028 –1.750 0.112   Analysis of Variance   Source DF SS MS F p-value   Regression 5 2197.68 439.5 9.68 0.000   Residual Error 59 2679.56...